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The problem asks to evaluate the function \( (f - g)(0) \), given the functions:

\[
f(x) = x + 3
\]
\[
g(x) = x^2 - 2
\]

### Step-by-Step Solution:

1. **Set up the expression** for \( (f - g)(x) \):
   \[
   (f - g)(x) = f(x) - g(x)
   \]
   So, we subtract the functions:
   \[
   (f - g)(x) = (x + 3) - (x^2 - 2)
   \]

2. **Simplify** the expression:
   \[
   (f - g)(x) = x + 3 - x^2 + 2
   \]
   \[
   (f - g)(x) = -x^2 + x + 5
   \]

3. **Substitute** \( x = 0 \) into \( (f - g)(x) \):
   \[
   (f - g)(0) = -0^2 + 0 + 5
   \]
   \[
   (f - g)(0) = 5
   \]

Thus, \( (f - g)(0) = 5 \).

Would you like more details or have any questions?

### Related Questions:
1. What is the general expression for \( (f + g)(x) \)?
2. How do you find the derivative of \( f(x) \) and \( g(x) \)?
3. What is the result of \( (f \cdot g)(0) \)?
4. What is the result of \( \frac{f}{g}(0) \)?
5. How does \( f(x) \) intersect with \( g(x) \) graphically?

### Tip:
Always simplify the expressions before substituting values to make calculations easier.

Evaluate (f - g)(0) given f(x) = x + 3 and g(x) = x^2 - 2

Learn how to evaluate the function (f - g)(0) given f(x) = x + 3 and g(x) = x^2 - 2. A step-by-step guide simplifying the function and substituting values. Suitable for students in Grades 9-10.

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